CONTENTSIntroduction................................................................................................................................................. 3I. TERMS AND NOTATION....................................................................................................................... 5II. GROUPOIDS AND CATEGORIES...................................................................................................... 61. The notion of groupoid......................................................................................................................... 62. Equivalence of the definition of groupoid to the definition of Ehresmann.................................. 83. Relationship between l.lio notion of an liliroHiminn groupoid and the notion of a Brandt,groupoid...................................................................................................................................................... 94. Categories of functions and representation theorems................................................................. 125. The algebraic product of sets and the closure of a sot in the multiplicative system............... 15III. THE RELATIONSHIP BETWEEN A GOŁĄB PSEUDOOROUP AND AN EHRESMANN GROUPOID............................................................................................................... 166. The notions of a Gołąb pseudogroup and of a functional element............................................ 167. The isomorphism of an arbitrary Ehresmann groupoid and a Gołąbpseudogroup of a certain type. Groupoids of functional elements................................................. 18IV. GENERATING IN GOŁĄB PSEUDOGROUPS AND SOME PROPERTIES OF A SET OF FUNCTIONS.............................................................................................................................. 208. Some operations with sets of functions........................................................................................... 219. A quasi-order of the family of all subsets of the set, L (X)............................................................. 2410. Determining a pseudogroups with the aid of sets of functional elements............................. 2611. The problom of the existence of the smallest pseudogroup including a given setof local homeomorphisms...................................................................................................................... 29V. SEMI-PSEUDOGROUPS AND A GENERALIZATION OP THE NOTION OF AN ANALYTICAL STRUCTURE................................................................................................................ 3312. Semi-pseudogroups......................................................................................................................... 3313. The notion of an analytical structure............................................................................................... 35References................................................................................................................................................. 39
@book{bwmeta1.element.desklight-04b90e52-7961-4a82-9e02-abd6e4dc4aba,
author = {W. Waliszewski},
title = {Categories, groupoids, pseudogroups and analytical structures},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1965},
zbl = {0136.44401},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.desklight-04b90e52-7961-4a82-9e02-abd6e4dc4aba}
}
W. Waliszewski. Categories, groupoids, pseudogroups and analytical structures. GDML_Books (1965), http://gdmltest.u-ga.fr/item/bwmeta1.element.desklight-04b90e52-7961-4a82-9e02-abd6e4dc4aba/